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On the zeros of a conformal vector field

Published online by Cambridge University Press:  22 January 2016

David E. Blair
David E. Blair*
Affiliation:
Michigan State University
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In [1] S. Kobayashi showed that the connected components of the set of zeros of a Killing vector field on a Riemannian manifold (Mn,g) are totally geodesic submanifolds of (Mn,g) of even codimension including the case of isolated singular points. The purpose of this short note is to give a simple proof of the corresponding result for conformal vector fields on compact Riemannian manifolds. In particular we prove the following

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 55 , November 1974 , pp. 1 - 3
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Kobayashi, S., Fixed points of isometries, Nagoya Math. J. 13 (1958) 63–68.Google Scholar
[2] Obata, M., The conjectures on conformal transformations of Riemannian manifolds, J. Diff. Geom. 6 (1971) 247–258.Google Scholar
[3] Obata, M., Conformal transformations of Riemannian manifolds, J. Diff. Geom. 4 (1970) 311–333.Google Scholar